Compound Inequalities

AND (intersection): x must satisfy BOTH conditions. Written as: a < x < b or "x > a AND x < b" Graph: a segment between two values. OR (union): x must satisfy AT LEAST ONE condition. Written as: "x < a OR x > b" Graph: two rays going in opposite directions. The SAT mostly tests AND (double inequalities).

A double inequality like 3 < 2x + 1 < 11 means: [formula] Shortcut: solve all three parts at once — apply the same operation to all three sections.

Example: Solve 3 < 2x + 1 < 11